Create gold_mine_problem.py

Author: abhisheks008

Dynamic Programming/Gold Mine Problem/gold_mine_problem.py

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+# Python program to solve
+# Gold Mine problem
+
+# Problem Statement : Returns maximum amount of
+#                     gold that can be collected
+#                     when journey started from
+#                     first column and moves
+#                     allowed are right, right-up
+#                     and right-down
+ 
+# ----------------------------------------------------------------- 
+
+# Approach : Brute Force Method
+# Abhishek S, 2021
+
+# ----------------------------------------------------------------- 
+
+MAX = 100
+ 
+
+def getMaxGold(gold, m, n):
+ 
+    # Create a table for storing
+    # intermediate results
+    # and initialize all cells to 0.
+    # The first row of
+    # goldMineTable gives the
+    # maximum gold that the miner
+    # can collect when starts that row
+    goldTable = [[0 for i in range(n)]
+                        for j in range(m)]
+ 
+    for col in range(n-1, -1, -1):
+        for row in range(m):
+ 
+            # Gold collected on going to
+            # the cell on the rigth(->)
+            if (col == n-1):
+                right = 0
+            else:
+                right = goldTable[row][col+1]
+ 
+            # Gold collected on going to
+            # the cell to right up (/)
+            if (row == 0 or col == n-1):
+                right_up = 0
+            else:
+                right_up = goldTable[row-1][col+1]
+ 
+            # Gold collected on going to
+            # the cell to right down (\)
+            if (row == m-1 or col == n-1):
+                right_down = 0
+            else:
+                right_down = goldTable[row+1][col+1]
+ 
+            # Max gold collected from taking
+            # either of the above 3 paths
+            goldTable[row][col] = gold[row][col] + max(right, right_up, right_down)
+                                                            
+    # The max amount of gold
+    # collected will be the max
+    # value in first column of all rows
+    res = goldTable[0][0]
+    for i in range(1, m):
+        res = max(res, goldTable[i][0])
+ 
+    return res
+     
+# Driver code
+gold = [[1, 3, 3],
+    [2, 1, 4],
+    [0, 6, 4]]
+ 
+m = 3
+n = 3
+print ("- Gold Mine Problem using Dynamic Programming -")
+print ("-----------------------------------------------")
+print ()
+print ("Output : ")
+print ("The maximum amount of Gold can be collected : ")
+print(getMaxGold(gold, m, n))
+
+
+# -------------------------------------------------------------------------
+
+# Output
+# - Gold Mine Problem using Dynamic Programming -
+# -----------------------------------------------
+
+# Output : 
+# The maximum amount of Gold can be collected : 
+# 12
+
+# -------------------------------------------------------------------------
+
+# Code contributed by, Abhishek S, 2021